The euro zone's economy grew by 0.1 percent in the third quarter of 2013, after emerging from the longest recession in continental Europe in over 40 years the previous quarter. Economic surveys for sectors including services and manufacturing appear to show that the recovery is gathering steam, with activity picking up in December.

Unemployment in the 17-member currency bloc, however, remains stubbornly high at 12.1 percent. While youth unemployment increased in November 2013, according to data released earlier this month, with 3.575 million under-25s without a job in the euro zone.

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Jose Manuel Barroso

Barroso, who is the head of the European Union's executive arm, however, highlighted that the region's periphery in particular had performed much better than critics had feared.

"Instead of a Greek exit - now we have new members joining the euro zone," he said.

Discussing health-care reform, innovation and America's energy future from Davos, Switzerland, with Gov. Rick Perry, R-Texas. For the world to continue to grow, Saudi Arabia needs to be a major player, Perry says.